DNSDDR= #Primary DNS
You have no static DNS servers defined. even using DHCP at least one must be defined as static in both the dialup ISP account and in the main setup. The easiest way to get this information filled in automatically is to run "setup" while running in Ethernet mode and just save the settings when it is connected to the Internet.
# [Network 0]
SDHCP=y #DHCP client
DHCPDNS=y #DNS via DHCP
IPADDR0= #IP address
NETWORK0= #Network address
BRDCAST0= #Broadcast address
As above if you run and then save the setup while connected in ethernet mode it will fill these extra fields out. Blank could be causing some problems.
As for dialup mode, the modem may have dialed. But I see no actual connection in the report. You might try a different INIT string for the modem. As I recall some of these modems required using "AT&F1" ir "AT&F0" rather than "ATZ" to get the modem to really connect. I would recommend enabling the PPP debugging options to help diagnose any issues.
[ root@router } setup -> System Settings -> On/Off debug & logging
dial-out chat logging = y
Enable diald logging = y
Enable dialup connection logging = y
Enable pppd logging = e
x and save the setup and then reboot. Make certain to ALWAYS make changes while in "Ethernet" mode and NEVER save the setup while in "dialup" mode because it will switch you main router type to the current mode the router is running in and really mess up your configuration.
After the above changes and changing the INIT string for the modem switch back to dialup mode and then change to "screen 3" when it dials the modem using "ALT+F3". There may also be information on other screen that is relevant, so try F3 through F7. regardless you should see the actual connection being negotiated and connected in the logs.
Also maker certain that in your BIOS that com1 which is cua0 is actually set to use IRQ 4. Because it is easy to have it configured for a non-standard IRQ and then it will not work properly. Even though it may seem to sort of work.
If you are afraid that you might make a mistake. The chances are high that you will never learn anything.